Kelvin

{{Short description|SI unit of temperature}} {{About|the unit of temperature|the person|Lord Kelvin|other uses}} {{Use dmy dates|date=January 2026|cs1-dates=y}} {{Use British English|date=November 2018}} {{Infobox Unit | name = kelvin  | image = Temperature-scales-comparison.svg{{!}}class=skin-invert-image | caption = Equivalent temperatures in the Kelvin (K), Celsius (°C), and Fahrenheit (°F) scales | standard = SI | quantity = temperature | symbol = K | namedafter = William Thomson, 1st Baron Kelvin | conversionslink = Conversions | calcinput = {{calculator|id=k|type=number|min=0|size=6|default=273.15}} | convertfromx = yes | units1 = Celsius | inunits1 = {{calculator|id=c|type=plain|size=9|NaN-text=?|formula=round(k-273.15,5)|default=0}} °C | units2 = Fahrenheit | inunits2 = {{calculator|id=f|type=plain|size=9|NaN-text=?|formula=round((k-273.15)*9/5+32,5)|default=32}} °F | units3 = Rankine scale | inunits3 = {{calculator|id=ra|type=plain|size=9|NaN-text=?|formula=round(k*1.8,5)|default=491.67}} °Ra | extraheader = | extralabel = 2019 definition | extradata = {{math|''k''B}} ≝ {{val|1.380649|e=-23}} J/K }}

The '''kelvin''' (symbol: '''K''') is the base unit for temperature in the International System of Units (SI). The '''Kelvin scale''' is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K.<ref name="MEP for kelvin 2019"/><ref name="SI Brochure 9"/><ref name="BIPM web page for kelvin"/><ref name="NIST SI redefinition"/> By definition, the units of the Celsius scale (symbol °C) and the Kelvin scale have the same magnitude (that is, a rise in temperature of one kelvin and a rise of 1 °C are both equal to 1 K), and any temperature in degrees Celsius can be converted to the kelvin scale by adding 273.15.<ref name="MEP for kelvin 2019" /><ref name="nist intro" />

The 19th-century British scientist Lord Kelvin first developed and proposed the scale.<ref name="nist intro"/> It was often called the "absolute Celsius" scale in the early 20th century.<ref name="absoluteC"/> The kelvin was formally added to the International System of Units in 1954, defining 273.16 K to be the temperature of the triple point of water (0.01 °C). The Celsius, Fahrenheit, and Rankine scales were redefined in terms of the Kelvin scale using this definition.<ref name="SI Brochure 9" /><ref name="Busting Myths about the Metric System" /><ref name="NIST HB44 Appendix C" /> The 2019 revision of the SI now defines the kelvin in terms of energy by setting the Boltzmann constant; every 1 K change of thermodynamic temperature corresponds to a change in the thermal energy, {{math|''k''B''T''}}, of ''exactly'' {{physconst|k|ref=no|symbol=no|unit=joules}}.<ref name="SI Brochure 9" />

== History == {{see also|Thermodynamic temperature#History}}

=== Precursors === [[File:Melting ice thermometer.jpg|thumb|An ice water bath offered a practical calibration point for thermometers (shown here in Celsius) before the physical nature of heat was well understood.]]

During the 18th century, multiple temperature scales were developed,<ref name="NIST kelvin history">{{cite journal |title=Kelvin: History |url=https://www.nist.gov/si-redefinition/kelvin-history |journal=NIST |date=14 May 2018 |access-date=21 February 2022}}</ref> notably Fahrenheit and Celsius. These scales predated much of the modern science of thermodynamics, including atomic theory and the kinetic theory of gases which underpin the concept of absolute zero. Instead, they chose defining points within the range of human experience that could be reproduced easily and with reasonable accuracy, but lacked any deep significance in thermal physics. In the case of the Celsius scale (and the long defunct Newton and Réaumur scales) the melting point of ice served as such a starting point, with Celsius being defined (from the 1740s to the 1940s) by calibrating a thermometer such that: * Water's freezing point is 0 °C. * Water's boiling point is 100 °C.

This definition assumes pure water at a specific pressure chosen to approximate the natural air pressure at sea level. Thus, an increment of 1 °C equals {{sfrac|1|100}} of the temperature difference between the melting and boiling points. The same temperature interval was later used for the Kelvin scale.

=== Charles's law === From 1787 to 1802, it was determined by Jacques Charles (unpublished), John Dalton,<ref name="Dalton_1801_1"/><ref name="Dalton_1801_2"/> and Joseph Louis Gay-Lussac<ref name="Gay-Lussac_1802"/> that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0 °C and 100 °C. Extrapolation of this law suggested that a gas cooled to about −273 °C would occupy zero volume.

=== Lord Kelvin === [[File:Baron Kelvin 1906.jpg|thumb|upright|Lord Kelvin, the namesake of the unit of measure.]]

==== First absolute scale ==== In 1848, William Thomson, who was later ennobled as Lord Kelvin, published a paper ''On an Absolute Thermometric Scale''.{{sfn|Thomson|1882|pp=100–106}} The scale proposed in the paper turned out to be unsatisfactory, but the principles and formulas upon which the scale was based were correct.<ref name="Magie">{{cite book |last1=Magie |first1=William Francis |title=A Source Book In Physics |date=1935 |page=237 |url=https://archive.org/details/in.ernet.dli.2015.449479/page/n251/mode/2up}}</ref> For example, in a footnote, Thomson derived the value of −273 °C for absolute zero by calculating the negative reciprocal of 0.00366—the coefficient of thermal expansion of an ideal gas per degree Celsius relative to the ice point.<ref>{{harvnb|Thomson|1882|p=104}}: "If we push the strict principle of graduation, stated above, sufficiently far, we should arrive at a point corresponding to the volume of air being reduced to nothing, which would be marked as −273° of the scale (−100/·366, if ·366 be the coefficient of expansion); and therefore −273° of the air-thermometer is a point which cannot be reached at any finite temperature, however low."</ref> This derived value agrees with the currently accepted value of −273.15 °C, allowing for the precision and uncertainty involved in the calculation.

The scale was designed on the principle that "a unit of heat descending from a body {{mvar|A}} at the temperature {{mvar|T}}° of this scale, to a body {{mvar|B}} at the temperature {{nowrap|({{mvar|T}} − 1)°}}, would give out the same mechanical effect, whatever be the number {{mvar|T}}."{{sfn|Thomson|1882|p=104}} Specifically, Thomson expressed the amount of work necessary to produce a unit of heat (the thermal efficiency) as <math>\mu(t) (1 + E t)/E</math>, where <math>t</math> is the temperature in Celsius, <math>E</math> is the coefficient of thermal expansion, and <math>\mu(t)</math> was "Carnot's function", a substance-independent quantity depending on temperature,{{sfn|Thomson|1882|p=187}} motivated by an obsolete version of Carnot's theorem.<ref name="Magie"/>{{sfn|Thomson|1882|p=106}} The scale is derived by finding a change of variables <math>T_{1848} = f(T)</math> of temperature <math>T</math> such that <math>dT_{1848} / dT</math> is proportional to <math>\mu</math>. thumb|Thermometer showing temperature in kelvin and degrees Celsius When Thomson published his paper in 1848, he only considered Regnault's experimental measurements of <math>\mu(t)</math>.{{sfn|Thomson|1882|p=193}} That same year, James Prescott Joule suggested to Thomson that the true formula for Carnot's function was{{sfn|Thomson|1882|p=212}} <math display="block">\mu(t) = J \frac{E}{1+E t},</math> where <math>J</math> is "the mechanical equivalent of a unit of heat",{{sfn|Thomson|1882|p=186}} now referred to as the specific heat capacity of water, approximately {{convert|771.8|ftlbf/F/lb|J/K/kg}}.{{sfn|Thomson|1882|p=192}} Thomson was initially sceptical of the deviations of Joule's formula from experiment, stating "I think it will be generally admitted that there can be no such inaccuracy in Regnault's part of the data, and there remains only the uncertainty regarding the density of saturated steam".{{sfn|Thomson|1882|pp=214–215}} Thomson referred to the correctness of Joule's formula as "Mayer's hypothesis", on account of it having been first assumed by Mayer.{{sfn|Thomson|1882|p=213}} Thomson arranged numerous experiments in coordination with Joule, eventually concluding by 1854 that Joule's formula was correct and the effect of temperature on the density of saturated steam accounted for all discrepancies with Regnault's data.{{sfn|Thomson|1882|p=388}} Therefore, in terms of the modern Kelvin scale <math>T</math>, the first scale could be expressed as follows:{{sfn|Thomson|1882|p=106}} <math display="block">T_{1848} = 100 \frac{\log(T / \text{273 K})}{\log(\text{373 K} / \text{273 K})}</math> The parameters of the scale were arbitrarily chosen to coincide with the Celsius scale at 0° and 100 °C or 273 and 373 K (the melting and boiling points of water).<ref>{{harvnb|Thomson|1882|p=105}}: "The arbitrary points which coincide on the two scales are 0° and 100°"</ref> On this scale, an increase of approximately 222 degrees corresponds to a doubling of Kelvin temperature, regardless of the starting temperature, and "infinite cold" (absolute zero) has a numerical value of negative infinity.<ref>{{cite journal |last1=Saslow |first1=WM |title=A History of Thermodynamics: The Missing Manual. |journal=Entropy |date=7 January 2020 |volume=22 |issue=1 |doi=10.3390/e22010077|doi-access=free |pmid=33285852|pmc=7516509 |bibcode=2020Entrp..22...77S |at=eqn. (36)}}</ref>

==== Modern absolute scale ====

Thomson understood that with Joule's proposed formula for <math>\mu</math>, the relationship between work and heat for a perfect thermodynamic engine was simply the constant <math>J</math>.{{sfn|Thomson|1882|p=190|loc=formula (7)|}} In 1854, Thomson and Joule thus formulated a second absolute scale that was more practical and convenient, agreeing with air thermometers for most purposes.{{sfn|Thomson|1882|pp=106,232–236}} Specifically, "the numerical measure of temperature shall be simply the mechanical equivalent of the thermal unit divided by Carnot's function."{{sfn|Thomson|1882|p=234}}

To explain this definition, consider a reversible Carnot cycle engine, where <math>Q_\mathrm{H}</math> is the amount of heat energy transferred into the system, <math>Q_\mathrm{C}</math> is the heat leaving the system, <math>W</math> is the work done by the system (<math>Q_\mathrm{H} - Q_\mathrm{C}</math>), <math>t_\mathrm{H}</math> is the temperature of the hot reservoir in degrees Celsius, and <math>t_\mathrm{C}</math> is the temperature of the cold reservoir in Celsius. The Carnot function is defined as <math>\mu =W / Q_\mathrm{H}(t_\mathrm{H} - t_\mathrm{C})</math>, and the absolute temperature as <math>T_\mathrm{H} = J/\mu</math>. One finds the relationship <math>T_\mathrm{H}= J Q_\mathrm{H} (t_\mathrm{H}-t_\mathrm{C})/W</math>. By supposing <math>T_\mathrm{H}-T_\mathrm{C}=J (t_\mathrm{H}-t_\mathrm{C})</math>, one obtains the general principle of an absolute thermodynamic temperature scale for the Carnot engine, <math>Q_\mathrm{H} / T_\mathrm{H} = Q_\mathrm{C} / T_\mathrm{C}</math>. The definition can be shown to correspond to the thermometric temperature of the ideal gas laws.<ref>{{cite book |last1=Wang |first1=Lin-Shu |title=A treatise of heat and energy |date=2020 |publisher=Springer |location=Cham |isbn=9783030057466 |page=77}}</ref>

This definition by itself is not sufficient. Thomson specified that the scale should have two properties:{{sfn|Thomson|1882|p=235}} * The absolute values of two temperatures are to one another in the proportion of the heat taken in to the heat rejected in a perfect thermodynamic engine working with a source and refrigerator at the higher and lower of the temperatures respectively. * The difference of temperatures between the freezing- and boiling-points of water under standard atmospheric pressure shall be called 100 degrees. (The same increment as the Celsius scale) Thomson's best estimates at the time were that the temperature of freezing water was 273.7 K and the temperature of boiling water was 373.7 K.{{sfn|Thomson|1882|p=236}}

These two properties would be featured in all future versions of the Kelvin scale, although it was not yet known by that name. In the early decades of the 20th century, the Kelvin scale was often called the "absolute Celsius" scale, indicating Celsius degrees counted from absolute zero rather than the freezing point of water, and using the same symbol for regular Celsius degrees, °C.<ref name="absoluteC">''Encyclopaedia Britannica'' editions from the 1920s and 1950s, the article "Planets".</ref>

=== Triple point standard === [[Image:Phase-diag2.svg|class=skin-invert-image|thumb|upright=1.5|A typical phase diagram. The solid green line applies to most substances; the dashed green line gives the anomalous behaviour of water. The boiling line (solid blue) runs from the triple point to the critical point, beyond which further increases in temperature and pressure produce a supercritical fluid.]] In 1873, William Thomson's older brother James coined the term ''triple point''<ref>{{Cite journal|last=Thomson|first=James|date=1873|title=A quantitative investigation of certain relations between the gaseous, the liquid, and the solid states of water-substance|journal=Proceedings of the Royal Society of London|url=https://babel.hathitrust.org/cgi/pt?id=hvd.32044106377062&view=1up&seq=48|volume=22|page=28|bibcode=1873RSPS...22...27T |issn=0370-1662|quote=and consequently that the three curves would meet or cross each other in one point, which I have called the ''triple point''.}}</ref> to describe the combination of temperature and pressure at which the solid, liquid, and gas phases of a substance were capable of coexisting in thermodynamic equilibrium. While any two phases could coexist along a range of temperature-pressure combinations (e.g. the boiling point of water can be affected quite dramatically by raising or lowering the pressure), the triple point condition for a given substance can occur only at a single pressure and only at a single temperature. By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use.

In 1948, the Celsius scale was recalibrated by assigning the triple point temperature of water the value of 0.01 °C exactly<ref name=":0">{{Cite journal |last=Swinton |first=F. L. |date=September 1967 |title=The triplet point of water |url=https://pubs.acs.org/doi/abs/10.1021/ed044p541 |journal=Journal of Chemical Education |language=en |volume=44 |issue=9 |pages=541 |doi=10.1021/ed044p541 |bibcode=1967JChEd..44..541S |issn=0021-9584|url-access=subscription }}</ref> and allowing the melting point at standard atmospheric pressure to have an empirically determined value (and the actual melting point at ambient pressure to have a fluctuating value) close to 0 °C. This was justified on the grounds that the triple point was judged to give a more accurately reproducible reference temperature than the melting point.<ref name="CGPM 9 res 3 (1948)">{{cite web |title=Resolution 3 of the 9th CGPM (1948) |url=https://www.bipm.org/en/committees/cg/cgpm/9-1948/resolution-3 |publisher=BIPM |access-date=21 February 2022}}</ref> The triple point could be measured with ±0.0001 °C accuracy, while the melting point just to ±0.001 °C.<ref name=":0" />

In 1954, with absolute zero having been experimentally determined to be about −273.15 °C per the definition of °C then in use, Resolution 3 of the 10th General Conference on Weights and Measures (CGPM) introduced a new internationally standardized Kelvin scale which defined the triple point as exactly 273.15 + 0.01 = 273.16 degrees Kelvin.<ref name="CGPM 10 res 3 (1954)">{{cite web |title=Resolution 3 of the 10th CGPM (1954) |url=https://www.bipm.org/en/committees/cg/cgpm/10-1954/resolution-3 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name=res310>{{cite web |title=Resolution 3: Definition of the thermodynamic temperature scale |work=Resolutions of the 10th CGPM |publisher=Bureau International des Poids et Mesures |url=http://www.bipm.fr/en/CGPM/db/10/3/ |year=1954 |access-date=6 February 2008 |url-status=dead |archive-url=https://web.archive.org/web/20070623215318/http://www.bipm.fr/en/CGPM/db/10/3/ |archive-date=23 June 2007}}</ref>

In 1967/1968, Resolution 3 of the 13th CGPM renamed the unit increment of thermodynamic temperature "kelvin", symbol K, replacing "degree Kelvin", symbol {{not a typo|°K}}.<ref name="CGPM 13 res 3 (1967)" /><ref name=res313>{{cite web |title=Resolution 3: SI unit of thermodynamic temperature (kelvin) |work=Resolutions of the 13th CGPM |url=http://www.bipm.fr/en/CGPM/db/13/3/ |publisher=Bureau International des Poids et Mesures |year=1967 |access-date=6 February 2008 |url-status=dead |archive-url=https://web.archive.org/web/20070421013852/http://www.bipm.fr/en/CGPM/db/13/3/ |archive-date=21 April 2007}}</ref> The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction {{sfrac|273.16}} of the thermodynamic temperature of the triple point of water."<ref name="NIST SI redefinition" /><ref name="CGPM 13 res 4 (1967)">{{cite web |title=Resolution 4 of the 13th CGPM (1967) |url=https://www.bipm.org/en/committees/cg/cgpm/13-1967/resolution-4 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name="res413">{{cite web|url=https://www.bipm.org/en/CGPM/db/13/4/|title=Resolution 4: Definition of the SI unit of thermodynamic temperature (kelvin)|year=1967|work=Resolutions of the 13th CGPM|publisher=Bureau International des Poids et Mesures|archive-url=https://web.archive.org/web/20070615125646/http://www.bipm.fr/en/CGPM/db/13/4/|archive-date=15 June 2007|url-status=dead |access-date=6 February 2008}}</ref>

After the 1983 redefinition of the metre, this left the kelvin, the second, and the kilogram as the only SI units not defined with reference to any other unit.

In 2005, noting that the triple point could be influenced by the isotopic ratio of the hydrogen and oxygen making up a water sample and that this was "now one of the major sources of the observed variability between different realizations of the water triple point", the International Committee for Weights and Measures (CIPM), a committee of the CGPM, affirmed that for the purposes of delineating the temperature of the triple point of water, the definition of the kelvin would refer to water having the isotopic composition specified for Vienna Standard Mean Ocean Water.<ref name="NIST SI redefinition" /><ref name="CGPM 23 res 10 (2007)">{{cite web |title=Resolution 10 of the 23rd CGPM (2007) |url=https://www.bipm.org/en/committees/cg/cgpm/23-2007/resolution-10 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name=sib2115>{{cite web|title=Unit of thermodynamic temperature (kelvin) |work=SI Brochure, 8th edition |at=Section 2.1.1.5 |url=http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html |publisher=Bureau International des Poids et Mesures |year=1967 |access-date=6 February 2008 |url-status=dead |archive-url=https://web.archive.org/web/20070926215600/http://www1.bipm.org/en/si/si_brochure/chapter2/2-1/2-1-1/kelvin.html |archive-date=26 September 2007 }}</ref>

=== 2019 redefinition === {{further|2019 revision of the SI}} [[File:Unit relations in the new SI black arrows to K.svg|class=skin-invert-image|thumb|280x280px|2019 SI unit dependencies. The kelvin (K) is now fixed in terms of the Boltzmann constant ({{math|''k''B}}) and the joule. The joule is not shown because it is a derived unit defined by the metre (m), second (s), and kilogram (kg). Those SI base units are themselves defined by the universal constants of the speed of light (''{{mvar|c}}''), the caesium-133 hyperfine transition frequency ({{math|Δ''ν''Cs}}) and the Planck constant (''{{mvar|h}}''). Black arrows trace the dependencies from these constants to the kelvin.]] The Boltzmann constant {{math|''k''B}} serves as the bridge in the relation {{math|1= ''E'' = ''k''B''T''}}, linking characteristic microscopic energies to the macroscopic temperature scale.<ref name=Kalinin>{{cite journal | doi = 10.1007/s11018-005-0195-9 |last1=Kalinin |first1=M. |last2=Kononogov |first2=S. | title = Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility | journal = Measurement Techniques | pages = 632–636 | volume = 48 | issue = 7 | year = 2005|bibcode=2005MeasT..48..632K |s2cid=118726162 }}</ref> In the International System of Units (SI), the kelvin has traditionally been treated as an independent base unit with its own dimension. By contrast, in fundamental physics it is common to adopt natural units by setting the Boltzmann constant equal to unity, so that temperature and energy share the same units.<ref name=Kalinin/><ref>{{cite book |last1=Kittel |first1=Charles |last2=Kroemer |first2=Herbert |title=Thermal physics |date=1980 |publisher=W. H. Freeman |location=San Francisco |isbn=0716710889 |pages=41 |edition=2nd |quote=We prefer to use a more natural temperature scale ... the fundamental temperature has the units of energy.}}</ref>

In 2005, the CIPM began a programme to redefine the kelvin in terms of the Boltzmann constant, alongside exploring new definitions for several other SI base units in terms of fundamental constants. The motivation was to allow more accurate measurements at temperatures far away from the triple point of water, and to be independent from any particular substance or measurement.<ref name="Fischer2007">{{cite web | url = http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Report_to_CIPM_2.pdf | title = Report to the CIPM on the implications of changing the definition of the base unit Kelvin | display-authors=1 | vauthors = Fischer J, Gerasimov S, Hill KD, Machin G, Moldove M, Pitre L, Steur P, Stock M, Tamura O, Ugur H, White DR, Yang I, Zhang J | publisher = International Committee for Weights and Measures (CIPM) | publication-date = 2 May 2007 | archive-url=https://web.archive.org/web/20120208183926/http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Report_to_CIPM_2.pdf | archive-date = 8 February 2012}}</ref> Originally slated for adoption in 2011 with the Boltzmann constant being {{val|1.38065|end=''X''|e=-23|u=J|up=K}}, ''X'' to be determined,<ref name="draft"> {{cite web |url=http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf |title=Draft Chapter 2 for SI Brochure, following redefinitions of the base units |author=Ian Mills |publisher=CCU |website=BIPM |date=29 September 2010 |access-date=1 January 2011 |url-status=dead |archive-url=https://web.archive.org/web/20110110104615/http://www.bipm.org/utils/en/pdf/si_brochure_draft_ch2.pdf |archive-date=10 January 2011 }}</ref> concerns arose about maintaining the precision of the triple point, and the redefinition was postponed until such time as more accurate measurements could be made, with these experiments taking several years in some cases.<ref> {{cite press release | url = http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf | title = General Conference on Weights and Measures approves possible changes to the International System of Units, including redefinition of the kilogram. | publisher = General Conference on Weights and Measures | location = Sèvres, France | date = 23 October 2011 | access-date = 25 October 2011 | url-status = dead | archive-url = https://web.archive.org/web/20120209175127/http://www.bipm.org/utils/en/pdf/Press_release_resolution_1_CGPM.pdf | archive-date = 9 February 2012 }}</ref><ref> {{Cite web |url=http://www.bipm.org/cc/TGFC/Allowed/Minutes/CODATA_Minutes_14-BIPM-public.pdf |title=Report on the Meeting of the CODATA Task Group on Fundamental Constants |date=3–4 November 2014 |place=BIPM |first=B. |last=Wood |page=3 |url-status=dead |archive-url=https://web.archive.org/web/20151013174929/http://www.bipm.org/cc/TGFC/Allowed/Minutes/CODATA_Minutes_14-BIPM-public.pdf |archive-date=13 October 2015 }} "Molar gas constant R and Boltzmann constant k"</ref> Ultimately, the kelvin redefinition became part of the larger 2019 revision of the SI. In late 2018, the 26th General Conference on Weights and Measures (CGPM) adopted the value of {{math|''k''B}} = {{physconst|k}}<ref name="draft" /><ref name="MEP for kelvin 2019" /><ref name="SI Brochure 9" /><ref name="NIST SI redefinition" /><ref name="CGPM 26 res 1 (2018)" /> and the new definition officially came into force on 20 May 2019, the 144th anniversary of the Metre Convention.<ref name="CGPM 26 res 1 (2018)">{{cite web |title=Resolution 1 of the 26th CGPM (2018) |url=https://www.bipm.org/en/committees/cg/cgpm/26-2018/resolution-1 |publisher=BIPM |access-date=21 February 2022}}</ref><ref name="MEP for kelvin 2019" /><ref name="SI Brochure 9" /><ref name="NIST SI redefinition" />

With this new definition, the kelvin now only depends on the Boltzmann constant and universal constants (see 2019 SI unit dependencies diagram), allowing the kelvin to be expressed as:<ref name="SI Brochure 9" /> : 1 kelvin = {{Nowrap|{{sfrac|{{val|1.380649|e=-23}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}} {{Math|{{sfrac|{{gaps|''h''|Δ''ν''Cs}}|''k''B}}}}}} ≈ {{Nowrap|{{val|2.2666653}} {{Math|{{sfrac|{{gaps|''h''|Δ''ν''Cs}}|''k''B}}}}}}.

In practical terms, as was the goal,<ref name="Fischer2007"/> the change went largely unnoticed: the chosen value has enough accuracy and significant figures for continuity, ensuring that water still freezes at 0 °C to high precision.<ref>{{cite web |url=http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Updating_the_definition_of_the_kelvin2.pdf |title=Updating the definition of the kelvin |publisher=BIPM |access-date=23 February 2010 |url-status=dead |archive-url=https://web.archive.org/web/20081123043044/http://www.bipm.org/wg/CCT/TG-SI/Allowed/Documents/Updating_the_definition_of_the_kelvin2.pdf |archive-date=23 November 2008}}</ref> The difference lies in the status of reference points. Before the redefinition, the triple point of water was taken as exact, while the Boltzmann constant had a measured value of {{val|1.38064903|(51)|e=-23|u=J|up=K}}, with a relative standard uncertainty of {{val|3.7|e=-7}}.<ref name=codata2017> {{cite journal |title=The CODATA 2017 values of ''h'', ''e'', ''k'', and ''N''A for the revision of the SI |collaboration=Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants |first1=D B |last1=Newell |first2=F |last2=Cabiati |first3=J |last3=Fischer |first4=K |last4=Fujii |first5=S G |last5=Karshenboim |first6=H S |last6=Margolis |first7=E |last7=de Mirandés |first8=P J |last8=Mohr |first9=F |last9=Nez |first10=K |last10=Pachucki |first11=T J |last11=Quinn |first12=B N |last12=Taylor |first13=M |last13=Wang |first14=B M |last14=Wood |first15=Z |last15=Zhang |journal=Metrologia |volume=55 |issue=1 |pages=L13–L16 |date=29 January 2018 |doi=10.1088/1681-7575/aa950a |bibcode=2018Metro..55L..13N |doi-access=free |bibcode-access=free }}</ref> Afterward, the Boltzmann constant was exact and the uncertainty is transferred to the triple point of water, which is now {{val|273.1600|(1)|u=K}}.{{efn|name=uncertainty|The absolute uncertainty can be calculated as {{math|273.16 × {{val|3.7|e=-7|u=K}}}}, which can be rounded to {{val|0.10|u=mK}} for all practical purposes.<ref>{{cite journal |last1=Fischer |first1=J |last2=Fellmuth |first2=B |last3=Gaiser |first3=C |last4=Zandt |first4=T |last5=Pitre |first5=L |last6=Sparasci |first6=F |last7=Plimmer |first7=M D |last8=de Podesta |first8=M |last9=Underwood |first9=R |last10=Sutton |first10=G |last11=Machin |first11=G |last12=Gavioso |first12=R M |last13=Madonna Ripa |first13=D |last14=Steur |first14=P P M |last15=Qu |first15=J |last16=Feng |first16=X J |last17=Zhang |first17=J |last18=Moldover |first18=M R |last19=Benz |first19=S P |last20=White |first20=D R |last21=Gianfrani |first21=L |last22=Castrillo |first22=A |last23=Moretti |first23=L |last24=Darquié |first24=B |last25=Moufarej |first25=E |last26=Daussy |first26=C |last27=Briaudeau |first27=S |last28=Kozlova |first28=O |last29=Risegari |first29=L |last30=Segovia |first30=J J |last31=Martín |first31=M C |last32=del Campo |first32=D |title=The Boltzmann project |journal=Metrologia |date=1 April 2018 |volume=55 |issue=2 |pages=R1–R20 |doi=10.1088/1681-7575/aaa790 |pmid=31080297|pmc=6508687|bibcode=2018Metro..55R...1F }}</ref>}}

On a deeper level, the kelvin is now defined in terms of the joule, making the separate existence of a temperature dimension theoretically unnecessary. The kelvin could have been redefined as a non-coherent derived SI unit, with {{math|1= 1 K = {{val|1.380649|e=-23|u=J}}}}.<ref name=Kalinin/><ref>{{cite journal |last1=Mohr |first1=Peter J. |last2=Shirley |first2=Eric L. |last3=Phillips |first3=William D. |last4=Trott |first4=Michael |title=On the dimension of angles and their units |journal=Metrologia |date=1 October 2022 |volume=59 |issue=5 |pages=053001 |doi=10.1088/1681-7575/ac7bc2|arxiv=2203.12392|bibcode=2022Metro..59e3001M |doi-access=free|quote=The scientific community could have decided to have a unit system in which temperature is measured in joules, but we find it to be more convenient to measure temperature in kelvins.}}</ref> Yet, "for historical and especially practical reasons, the kelvin will continue to be a base unit of the SI".<ref>{{cite journal |last1=Fellmuth |first1=B. |last2=Fischer |first2=J. |last3=Machin |first3=G. |last4=Picard |first4=S. |last5=Steur |first5=P. P. M. |last6=Tamura |first6=O. |last7=White |first7=D. R. |last8=Yoon |first8=H. |title=The kelvin redefinition and its mise en pratique |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 March 2016 |volume=374 |issue=2064 |doi=10.1098/rsta.2015.0037|doi-access=free |pmid=26903103 |bibcode=2016RSPTA.37450037F }}</ref>

== Practical uses == [[File:Kelvin Temperature Chart Vertical tightened.svg|thumb|390x390px|Colour temperature (right) of various light sources (left)]]

=== Colour temperature === {{see also|Stefan–Boltzmann constant}} The kelvin is often used as a measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light with a frequency distribution characteristic of its temperature. Black bodies at temperatures below about {{val|4000|u=K}} appear reddish, whereas those above about {{val|7500|u=K}} appear bluish. Colour temperature is important in the fields of image projection and photography, where a colour temperature of approximately {{val|5600|u=K}} is required to match "daylight" film emulsions.

In astronomy, the stellar classification of stars and their place on the Hertzsprung–Russell diagram are based, in part, upon their surface temperature, known as effective temperature. The photosphere of the Sun, for instance, has an effective temperature of {{val|5772|u=K}}<ref>{{cite book | url=https://books.google.com/books?id=zT2HEAAAQBAJ&pg=PA216 | title=Astronomy: The Human Quest for Understanding | isbn=978-0-19-882582-1 | last1=Ostlie | first1=Dale A. | date=2022 | publisher=Oxford University Press }}</ref><ref>{{cite web | url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html | title=Sun Fact Sheet | access-date=19 February 2022 | archive-date=22 February 1998 | archive-url=https://web.archive.org/web/19980222081658/https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html | url-status=dead }}</ref><ref>{{cite book | url=https://books.google.com/books?id=2QBBEAAAQBAJ&dq=5772+K&pg=PA51 | title=Stories of Astronomers and Their Stars | isbn=978-3-030-80309-4 | last1=Falkner | first1=David E. | date=2 September 2021 | publisher=Springer }}</ref><ref>{{cite journal | arxiv=1605.09788 | doi=10.3847/0004-6256/152/2/41 | doi-access=free | title=NOMINAL VALUES FOR SELECTED SOLAR AND PLANETARY QUANTITIES: IAU 2015 RESOLUTION B3* † | date=2016 | last1=Prša | first1=Andrej | last2=Harmanec | first2=Petr | last3=Torres | first3=Guillermo | last4=Mamajek | first4=Eric | last5=Asplund | first5=Martin | last6=Capitaine | first6=Nicole | last7=Christensen-Dalsgaard | first7=Jørgen | last8=Depagne | first8=Éric | last9=Haberreiter | first9=Margit | last10=Hekker | first10=Saskia | last11=Hilton | first11=James | last12=Kopp | first12=Greg | last13=Kostov | first13=Veselin | last14=Kurtz | first14=Donald W. | last15=Laskar | first15=Jacques | last16=Mason | first16=Brian D. | last17=Milone | first17=Eugene F. | last18=Montgomery | first18=Michele | last19=Richards | first19=Mercedes | last20=Schmutz | first20=Werner | last21=Schou | first21=Jesper | last22=Stewart | first22=Susan G. | journal=The Astronomical Journal | volume=152 | issue=2 | page=41 }}</ref> as adopted by IAU 2015 Resolution B3.

Digital cameras and photographic software often use colour temperature in K in edit and setup menus. The simple guide is that higher colour temperature produces an image with enhanced white and blue hues. The reduction in colour temperature produces an image more dominated by reddish, "warmer" colours.

=== Kelvin as a unit of noise temperature === {{main|Noise figure}} For electronics, the kelvin is used as an indicator of how noisy a circuit is in relation to an ultimate noise floor, i.e. the noise temperature. The Johnson–Nyquist noise of resistors (which produces an associated ''kTC'' noise when combined with capacitors) is a type of thermal noise derived from the Boltzmann constant and can be used to determine the noise temperature of a circuit using the Friis formulas for noise.

== Derived units and SI multiples == {{main|Orders of magnitude (temperature)}}

The only SI derived unit with a special name derived from the kelvin is the degree Celsius. Like other SI units, the kelvin can also be modified by adding a metric prefix that multiplies it by a power of 10:

== Orthography == According to SI convention, the kelvin is never referred to nor written as a ''degree''. The word "kelvin" is not capitalized when used as a unit. It may be in plural form as appropriate (for example, "it is 283 kelvins outside", as for "it is 50 degrees Fahrenheit" and "10 degrees Celsius").<ref name="nist intro" /><ref name="plurals">{{citation |work=NIST SP 811 |title=NIST Guide to the SI {{!}} Chapter 9: Rules and Style Conventions for Spelling Unit Names |date=28 January 2016 |url=https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-9-rules-and-style-conventions-spelling-unit-names#97 |quote=A derived unit is usually singular in English, for example, the value 3 m2·K/W is usually spelled out as 'three square meter kelvin per watt', and the value 3 C·m2/V is usually spelled out as 'three coulomb meter squared per volt'. However, a 'single' unit may be plural; for example, the value 5 kPa is spelled out as 'five kilopascals', although 'five kilopascal' is acceptable. If in such a single-unit case the number is less than one, the unit is always singular when spelled out; for example, 0.5 kPa is spelled out as 'five-tenths kilopascal'. }}</ref><ref>{{Cite web |title=Definition of KELVIN |url=https://www.merriam-webster.com/dictionary/kelvin |access-date=21 August 2023 |website=Merriam-Webster.com }}</ref><ref>{{Cite book |url=https://translation-council-support-group.web.cern.ch/sites/default/files/styles/large/CERN%20TM%20English%20language%20style%20guide.pdf |title=CERN English Language Style Guide |publisher=CERN |year=2022 |pages=64}}</ref> The unit's symbol K is a capital letter,<ref name="CGPM 13 res 3 (1967)">{{cite web |title=Resolution 3 of the 13th CGPM (1967) |url=https://www.bipm.org/en/committees/cg/cgpm/13-1967/resolution-3 |publisher=BIPM |access-date=21 February 2022}}</ref> per the SI convention to capitalize symbols of units derived from the name of a person.<ref>{{Cite journal |date=13 January 2010 |title=Writing with SI (Metric System) Units |url=https://www.nist.gov/pml/owm/writing-si-metric-system-units |journal=NIST }}</ref> It is common convention to capitalize Kelvin when referring to Lord Kelvin<ref name="nist intro" /> or the Kelvin scale.<ref>{{cite book |last1=Brady |first1=James E. |last2=Senese |first2=Fred |title=Chemistry, Student Study Guide: The Study of Matter and Its Changes |date=28 January 2008 |publisher=John Wiley & Sons |isbn=978-0-470-18464-6 |page=15 |url=https://books.google.com/books?id=zS1EX-e7kPQC&pg=PA15 }}</ref>

The unit symbol K is encoded in Unicode at code point {{unichar|212A|kelvin sign}}. However, this is a compatibility character provided for compatibility with legacy encodings. The Unicode standard recommends using {{unichar|004B|latin capital letter k}} instead; that is, a normal capital K. "Three letterlike symbols have been given canonical equivalence to regular letters: {{unichar|2126|ohm sign}}, {{unichar|212A|kelvin sign}}, and {{unichar|212B|angstrom sign}}. In all three instances, the regular letter should be used."<ref>{{cite book|title=The Unicode Standard, Version 8.0|date=August 2015|location=Mountain View, California, US |publisher=The Unicode Consortium |isbn=978-1-936213-10-8|section=22.2|url=https://www.unicode.org/versions/Unicode8.0.0/ch22.pdf|access-date=6 September 2015|url-status=live|archive-url=https://web.archive.org/web/20161206230132/http://www.unicode.org/versions/Unicode8.0.0/ch22.pdf|archive-date=6 December 2016}}</ref>

== See also == {{Portal|Energy}} * Comparison of temperature scales * International Temperature Scale of 1990 * kT (energy) – product of the Boltzmann constant and temperature * Negative temperature * Outline of metrology and measurement Obsolete temperature scales include: * Rømer scale * Réaumur scale * Delisle scale * Newton scale * Leiden scale

== Notes == {{notelist}}

== References == {{Reflist|refs= <ref name="SI Brochure 9">{{cite web |title=SI Brochure: The International System of Units (SI) – 9th edition (updated in 2022) |url=https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf/2d2b50bf-f2b4-9661-f402-5f9d66e4b507 |publisher=BIPM |access-date=7 September 2022}}</ref> <ref name="BIPM web page for kelvin">{{cite web |title=SI base unit: kelvin (K) |url=https://www.bipm.org/en/si-base-units/kelvin |publisher=BIPM |access-date=5 March 2022}}</ref> <ref name="NIST SI redefinition">{{cite journal |title=A Turning Point for Humanity: Redefining the World's Measurement System |url=https://www.nist.gov/si-redefinition/turning-point-humanity-redefining-worlds-measurement-system |journal=NIST |date=12 May 2018 |access-date=21 February 2022}}</ref> <ref name="MEP for kelvin 2019">{{cite web |last=BIPM |date=20 May 2019 |title=Mise en pratique for the definition of the kelvin in the SI |url=https://www.bipm.org/documents/20126/41489682/SI-App2-kelvin.pdf/cd36cb68-3f00-05fd-339e-452df0b6215e?version=1.5&t=1637237805352&download=false |access-date=18 February 2022 |website=BIPM.org}}</ref> <ref name="nist intro">{{cite web |title=Kelvin: Introduction |url=https://www.nist.gov/si-redefinition/kelvin-introduction |website=NIST |access-date=2 September 2022 |language=en |date=14 May 2018}}</ref> <ref name="NIST HB44 Appendix C">{{cite web |title=Handbook 44 – 2026 – Appendix C – General Tables of Units of Measurement |url=https://nvlpubs.nist.gov/nistpubs/hb/2026/NIST.HB.44-2026.pdf#%5B%7B%22num%22%3A1217%2C%22gen%22%3A0%7D%2C%7B%22name%22%3A%22XYZ%22%7D%2C69%2C720%2C0%5D |website=nist.gov |publisher=NIST |access-date=23 February 2026}}</ref> <ref name="Busting Myths about the Metric System">{{cite journal |author-last=Benham |author-first=Elizabeth |title=Busting Myths about the Metric System |url=https://www.nist.gov/blogs/taking-measure/busting-myths-about-metric-system |journal=NIST |date=6 October 2020 |publisher=Taking Measure (official blog of the NIST) |access-date=21 February 2022}}</ref> <ref name="Dalton_1801_1">{{Cite journal |author-first=John |author-last=Dalton |date=1801 |url=https://books.google.com/books?id=3qdJAAAAYAAJ&pg=PA595 |title=Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air |journal=Memoirs of the Literary and Philosophical Society of Manchester |volume=5 part 2 |pages=550–574}}</ref> <ref name="Dalton_1801_2">{{Cite journal |author-first=John |author-last=Dalton |date=1801 |url=https://books.google.com/books?id=3qdJAAAAYAAJ&pg=PA595 |title=Essay IV. On the expansion of elastic fluids by heat |journal=Memoirs of the Literary and Philosophical Society of Manchester |volume=5 part 2 |pages=595–602}}</ref> <ref name="Gay-Lussac_1802">{{citation |author-last=Gay-Lussac |author-first=Joseph Louis |author-link=Joseph Louis Gay-Lussac |date=1802 |title=Recherches sur la dilatation des gaz et des vapeurs |journal=Annales de Chimie |volume=XLIII |page=137}}. [https://web.lemoyne.edu/~giunta/gaygas.html English translation (extract).]</ref> }}

== Bibliography == * {{cite web |author=Bureau International des Poids et Mesures |title=The International System of Units (SI) Brochure |version=9th Edition |publisher=International Committee for Weights and Measures |url=https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf |date=2019 |access-date=28 April 2022}} * {{cite book |last1=Thomson |first1=William (Lord Kelvin) |title=Mathematical and physical papers: Volume I |date=1882 |publisher=Cambridge University Press |url=https://archive.org/details/mathematicalphys01kelv}}

== External links == {{wiktionary}} * {{cite web |author-last=Thomson |author-first=William |title=On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's Observations |url=https://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html |website=zapatopi.net |publisher=Philosophical Magazine|date=October 1848 |access-date=21 February 2022|archive-url=https://web.archive.org/web/20080201095927/http://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html |archive-date=1 February 2008}} * {{cite web |author-last=Thomson |author-first=William |title=On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam |url=https://zapatopi.net/kelvin/papers/on_the_dynamical_theory_of_heat.html |website=zapatopi.net |publisher= Transactions of the Royal Society of Edinburgh|date=March 1851|access-date=5 May 2024}}

Category:1848 introductions Category:Scottish inventions Category:SI base units Category:William Thomson, 1st Baron Kelvin Category:Scales of temperature Category:Scales in meteorology